Formal:
* Sanctioned: Implies official permission or authorization.
* Authorized: Similar to sanctioned, suggesting formal approval.
* Ratified: Means formally confirmed or validated.
* Endorsed: Indicates support or approval, often from a prominent individual or group.
* Certified: Implies a formal process of verification and confirmation.
Informal:
* Okayed: A casual way of saying approved.
* Greenlit: Used in the context of projects or ideas, suggesting permission to proceed.
* Cleared: Implies that something has passed inspection or scrutiny.
* Accepted: Indicates that something has been received favorably.
* Passed: Often used for tests or proposals, implying success.
* Go-ahead: A phrase meaning permission to proceed.
Other:
* Granted: Used when something has been given or allowed.
* Condoned: Implies tolerance or acceptance, even if not explicitly approved.
* Acknowledged: Means that something has been noticed and accepted.
The best word to use will depend on the specific situation and the desired tone.